An adaptive weighted log-rank test with application to cancer prevention and screening trials

A class of adaptive weighted log-rank statistics is described where the vector of weights is chosen in a data-dependent way from a family of "smooth" weight vectors. A parametric family of weight vectors is identified which includes most shapes of weighting vectors that will be near optimal in many cancer prevention and screening trials. This family of weight vectors is used in an application of the proposed method to data from a breast cancer screening trial. Results from a small simulation study comparing the power of the adaptive statistic to that of the unweighted log-rank statistic are presented.